A key topic in differential fertility has been the effect of income on fertility. Almost invariably in such studies, the dependent variable is total number of children, or--in the case of grouped-data studies-- the average number of children. In a study of the U.S. 1960 Census data I found that husband's income apparently does not have the same effect on all birth orders. That is, the relationship is apparently curvilinear; higher husband's income leading to a higher probability of additional births when the family has few children but a lower probability of an additional birth when the family has many children. A crucial implication is that in studies whose dependent variable is total children ever born, or average children, the coefficient of income will not be meaningful. The result found in that previous study seems to the writer to be sufficiently novel and sufficiently important that this line of investigation should be followed up. The methods to be used include: (1) discriminant analysis on groups with exactly n versus exactly (n plus 1) children, in finely sub-classified cells within the 1960 U.S. census data; (2) gross-classification discriminant analysis using both exactly n versus (n plus 1) groups, and (n or less) versus ((n plus 1) or more) groups; (3) analyses of the sample taken as a single group, using dummy variables, if a statistical device to compare coefficients in samples with different proportions can be found; (4) other data bases than the U.S. census. These studies, together with the previous study, should yield a reasonably conclusive answer about whether the effect of income on an additional birth is curvilinear across birth orders, more income having first a positive and then a negative effect on family size. More solid knowledge about this phenomenon will also cast important light on the recent convergence of Americans to a 2-4 child family.